Relative Object Localization Process for Local Positioning System

ABSTRACT

Systems and methods for performing relative object localization using a local positioning system. The process in accordance with one embodiment solves the problem of determining the location (i.e., the position and orientation) of an object relative to a previous location of the object, or relative to another object, without the need for known 3-D data point positions in the environment. The process in accordance with another embodiment solves the problem of determining the location of the measurement instrument relative to a previous location of the measurement instrument using visible feature points on a target object as a reference, again without the need for known 3-D data point positions. The process in accordance with a further embodiment is capable of determining the locations of multiple objects relative to each other.

BACKGROUND

This disclosure generally relates to systems and methods for trackingthe locations of a movable target object (e.g., a robotic arm or otherelectro-mechanical machine that is guided by a computer program) as itmoves relative to a workpiece or part.

Applications involving manufacturing processes that use crawler vehiclesor other computer-controlled electro-mechanical machines often employlocation tracking in a reference coordinate system. Absolute motiontracking refers to tracking of position and/or orientation defined in areference coordinate system, such as an airplane coordinate system.

Pointing instruments that can highlight a position or region on a targetobject, in the local coordinate system of that object, can providevaluable point-of-use information for applications in areas such asautomated manufacturing. For example, a Local Positioning System (LPS)of the type disclosed in U.S. Pat. No. 7,859,655 (the disclosure ofwhich is incorporated by reference herein in its entirety) permits anoperator to acquire local coordinate measurement and imaging data for anobject in the field of view of the physical hardware of the LPS. An LPSmay use a pan-tilt unit to orient a camera in the direction of a targetobject for which local coordinates are needed. A laser range meter canbe used to measure range to the object, or distances can be entered orderived algorithmically. Image data, measured range data, and pan-tiltangles are used along with known calibration points to determine thelocation of the LPS device relative to the target object. With therelative location known, LPS measurements are converted into the localcoordinates of the target object's coordinate system (such as airplaneor building coordinates). An operator may control the pan-tilt unit,laser range meter, camera devices and other software operations of anLPS using keyboard controls, or interface devices such as joysticks,gamepad controllers, mouse devices, etc. The LPS includes a computersystem physically attached to, and collocated with, other components ofthe LPS.

The LPS disclosed in U.S. Pat. No. 7,859,655 uses known 3-D points on atarget object to perform an instrument-to-target calibration, afterwhich the system can be used to make measurements of other points orgroups of points in the coordinate system of the target object. Thisapproach for calibration works well if accurate 3-D point data isavailable for the target object; but in many potential use cases it isnot, which mean this mode of LPS operation cannot be used. Since theforegoing LPS process requires knowledge of 3-D data in the workenvironment, its use as a general-purpose measurement device is limitedto those cases where 3-D data is available.

Other processes for general-purpose measurement without use of known 3-Dreference data may involve: simple measurement tools, such as tapemeasures, measuring wheels, GPS or differential GPS, laser trackers, andsurveying equipment like theodolites and Total Stations. Some of thesesolutions can only measure point-to-point differences, and others canmeasure displacement vectors, but they are not configured to provideboth position and orientation for objects that have been moved. Othertracking systems, such as optical motion capture, can measure bothposition and orientation of one or more objects as those objects move,but motion capture systems require setup of multiple cameras in thetracking environment, which increases complexity and cost, and reducesthe portability of the system.

Other special-purpose devices may have some alignment capabilities, butthey are not set up for general-purpose usage. For example, machinetools like Coordinate Measuring Machines (CMMs) have internal processesthat perform similar tasks for alignment of the tool within the machineworkspace.

It would be advantageous to provide a process that addresses LPS usecases for situations where known 3-D points are not available forcalibration.

SUMMARY

The subject matter disclosed in detail hereinafter comprises systems andprocesses that address LPS use cases for situations where known 3-Dpoints are not available for calibration. In its basic form, the processenables the determination of position and orientation data of objectsrelative to an arbitrary reference location. Additional variations ofthe process address cases where a LPS has been repositioned and wheremultiple objects are being tracked.

The measurement method disclosed herein allows for a wider range of usesfor LPS and enables new types of applications involving relativelocation measurement. It can be used in applications such as roboticdevice localization and measurement system configuration. It can also beused for general-purpose point-to-point measurement applications. Inparticular, the measurement method disclosed herein enables rapidlocalization (position and orientation measurement) of large structures(such as an airplane fuselage or wing) relative to robotic arms ontracks that perform a non-destructive evaluation (NDE) scan of thestructure after it has been fabricated. Some future factories willrequire a method of orientation that can be done quickly. Themeasurement method disclosed herein also enables precise and rapidre-positioning of tooling or sensors, such as microwave sensors formeasuring paint thickness in between applications. In this case, it isimportant to be able to place the sensor back at the same measurementlocations on the surface between coats.

The system and process in accordance with one embodiment solves theproblem of determining the location (i.e., the position and orientation)of an object relative to a previous location of the object, or relativeto another object, without the need for known 3-D data point positionsin the environment. The system and process in accordance with anotherembodiment can be used to solve the problem of determining the locationof the measurement instrument relative to a previous location of themeasurement instrument using visible feature points on a target objectas a reference, again without need for known 3-D data point positions.The system and process in accordance with a further embodiment iscapable of determining the locations of multiple objects relative toeach other.

Some of the main differences between the measurement method disclosedherein as compared to the method used internally by CMMs is that themeasurement method disclosed herein is a portable application that canwork with any type of moveable object in any size environment; it doesnot contact the target object; it can be integrated into other machinecontrol systems; and can be manually operated or be part of an automatedapplication.

The relative object location or measurement instrument location datadetermined by the process described herein can be transmitted to otherdownstream processes for alignment or measurement purposes, or can bepresented through a computer user interface to guide an operator inaccomplishing measurement-related tasks. It can be used in a manualoperation mode or can use an image processing technique as part of anautomated measurement system.

Although the measurement method disclosed herein does not give resultsin the local coordinate system of the target object (as in the LPSprocess that uses known position data), it can give the position andorientation of an object relative to a starting location, which in manycases may be sufficient for the required task. For example, in somesituations a measurement process that had required absolute coordinatemeasurement may be reformulated into a process that can be performedwith only relative offset information. If the measurement task can bedefined in terms of position and orientation offsets from a referencelocation, such as visible landmarks, then the relative process presentedhere may be able to replace the absolute coordinate process (and known3-D data point positions are not needed).

One aspect of the subject matter disclosed in detail below is a methodfor determining a current position of a target object relative to aninitial location of the target object, where in this description“location” comprises a position and an orientation. This methodcomprises: (a) selecting a set of at least three non-collinear points ona target object; (b) placing the target object at an initial locationwithin measurement range of a positioning system (with a non-occludedview of the target points); (c) measuring respective coordinates ofthree points of the set of points associated with the target object in aframe of reference of the positioning system while the target object isat the initial location; (d) moving the target object from the initiallocation to a current location; (e) measuring respective coordinates ofthe three points associated with the target object in the frame ofreference of the positioning system while the target object is at thecurrent location; and (f) computing a position difference in a frame ofreference of the initial location of the target object based on resultsof steps (c) and (e), the position difference representing a differencebetween the initial and current positions of the target object in theframe of reference of the initial location of the target object. Inaccordance with some embodiments, step (f) further comprises computingan orientation difference in the frame of reference of the initiallocation of the target object based on the results of steps (c) and (e),the orientation difference representing a difference between the initialand current orientations of the target object in the frame of referenceof the initial location of the target object. The method may furthercomprise displaying results of step (f) to a user or sending results ofstep (f) to an application. When the number of points selected in step(a) is greater than three, step (c) further comprises measuringcoordinates of a fourth point, and the method further comprises:computing a second transformation matrix that defines the offset of thecurrent location of the target object relative to the initial locationof the target object; and multiplying the coordinates of the fourthpoint by the second transformation matrix.

Another aspect of the subject matter disclosed in detail below is amethod for determining a position of one target object relative toanother target object. This method comprises: (a) selecting a set of atleast three points on a first target object; (b) placing the firsttarget object at a first location within measurement range of apositioning system having a non-occluded view of the target points onthe first target object; (c) measuring respective coordinates of threepoints of the set of points on the first target object in a frame ofreference of the positioning system while the first target object is atthe first location; (d) selecting a set of at least three points on asecond target object; (e) placing the second target object at a secondlocation within measurement range of a positioning system having anon-occluded view of the target points on the second target object; (f)measuring respective coordinates of the three points on the secondtarget object in the frame of reference of the positioning system whilethe second target object is at the second location; and (g) computing afirst location difference in a frame of reference of the first locationof the first target object based on results of steps (c) and (f), thefirst location difference representing a difference between therespective locations of the first and second target objects in the frameof reference of the first location of the first target object. Thismethod may further comprise: (h) moving one or both of the first andsecond target objects and/or the positioning system from the initiallocation to a current location, the current location comprising acurrent position and a current orientation; (i) after step (h),measuring respective coordinates of the three points on the first andsecond target objects in the frame of reference of the positioningsystem; (j) computing a second location difference in a frame ofreference of the first location of the first target object based onresults of step (i), the second location difference representing adifference between the respective locations of the first and secondtarget objects in the frame of reference of the first location of thefirst target object; and (k) computing a third location difference in aframe of reference of the first location of the first target object, thethird location difference being based on a difference between the firstand second location differences. In accordance with one implementation,this method further comprises sending the results of step (k) to anotherprocess or application, such as a controller that controls the movementof one of the first and second target objects.

A further aspect is a method for locating a point on a target objectcomprising: (a) placing first instances of a positioning system and atarget object at respective locations such that the first instance of atarget object is within measurement range of the first instance of apositioning system; (b) selecting a set of at least three points on thefirst instance of a target object; (c) measuring respective coordinatesof three points of the set of points on the first instance of a targetobject in a frame of reference of the first instance of a positioningsystem while the first instances of a positioning system and a targetobject are at their respective locations; (d) placing second instancesof a positioning system and a target object at respective locations suchthat the second instance of a target object is within measurement rangeof the second instance of a positioning system; (e) measuring respectivecoordinates of three points of the set of points on the second instanceof a target object in a frame of reference of the second instance of apositioning system while the second instances of a positioning systemand a target object are at their respective locations; and (f) computinga displacement matrix that represents the change in the frame ofreference of the second instance of a positioning system with respect tothe frame of reference of the first instance of a positioning systembased on differences between the measurement results of steps (c) and(e); and (g) computing an updated calibration matrix representing atransformation from the frame of reference of the second instance of thepositioning system to a frame of reference of the second instance of thetarget object by multiplying a current calibration matrix by saiddisplacement matrix.

Yet another aspect of the subject matter disclosed below is a method forre-calibrating a positioning system with respect to a target object, themethod comprising: (a) selecting a set of at least three points on atarget object; (b) obtaining measurement results comprising respectivecoordinates of the set of points measured in the frame of reference of apositioning system while the positioning system is at a first location;(c) setting up the positioning system at a second location differentthan the first location; (d) measuring respective coordinates of thethree points of the set of points on the target object in the frame ofreference of the positioning system while the positioning system is atthe second location; (e) computing a displacement matrix based ondifferences between the obtained measurement results and the measurementresults of step (d); and (f) computing an updated calibration matrixrepresenting a transformation from the frame of reference of thepositioning system at the second location to a frame of reference of thetarget object by multiplying a calibration matrix corresponding to theobtained measurement results by the displacement matrix.

The concepts disclosed and embodied herein are not limited to use withlocal positioning systems, and it may be capable of working with similarorientation+distance measurement systems.

Other aspects of systems and methods for performing relative objectlocalization are disclosed below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing an isometric view of a physical setup inwhich a local positioning system is aimed at a target object for using abasic difference measurement method in accordance with one embodiment.

FIG. 2 is a flowchart showing data acquisition and processing steps fora basic location difference measurement method.

FIG. 3 is a flowchart showing steps of a process for measuring locationoffset when a set of three non-collinear points has moved.

FIG. 4 is a vector diagram for reference frame computation.

FIG. 5 is a flowchart showing steps of a process for recalibrating anLPS to re-target a set of points after the LPS instrument has beenmoved.

FIG. 6 is a flowchart showing data acquisition and processing steps in amethod of measuring location offset for multiple moving objects.

FIG. 7 is a diagram showing an isometric view of a physical setup inwhich a local positioning system is aimed at a robotic workcell withmultiple moving objects in accordance with another embodiment.

FIG. 8 is a flowchart showing steps of a process for measuring locationoffset for multiple moving objects.

FIG. 9 is a diagram showing example reference frame configurations formultiple moving objects.

Reference will hereinafter be made to the drawings in which similarelements in different drawings bear the same reference numerals.

DETAILED DESCRIPTION

The process for LPS usage described in detail herein is based onmeasurement of 3-D point positions relative to prior positions of thesame pattern of points. The 3-D points are defined relative to anarbitrary reference location and the local object coordinates of thesepoints do not need to be known prior to use of the method. The processuses the measured positions of a set of 3-D points in two or morelocations to determine the relative position and orientationdisplacement of the set of points.

Some LPS users have had difficulty acquiring the required 3-D data tomake the current LPS calibration process work, which limits the type ofapplications in which they could use LPS. Although multiple approachesto access 3-D data have been provided for objects in which 3-Dinformation is known, this 3-D data acquisition step takes time and canbe challenging in some situations. In some use cases 3-D data might notbe available, and for other cases, the as-built or modified object maydiffer enough from the as-designed 3-D CAD model of the object that acorrect calibration is not acquired, which may lead to measurementerrors.

The LPS calibration capability disclosed herein enables use of LPS forspecific types of measurement without requiring the input of known 3-Dpoints. Although this method does not provide direct measurement oflocal coordinates on the target object, it does provide the ability tomeasure changes between points or between sets of points—enabling alarge number of potential use cases. The ability to use LPS to measurechange in position and orientation from a reference location is the corecapability disclosed herein, and has led to several variations of themethod in applications associated with object alignment. The primaryvariations that will be discussed include: a) computing offsets for amoved object with a stationary LPS (and equivalently a stationary objectwith a moved LPS), b) re-targeted points of interest with a moved objectand/or a moved LPS, and c) computing offsets for multiple moved objects.

Method Details

The instrument calibration matrix is one of the foundation elements ofthe LPS process; it defines where the location of the LPS instrument isrelative to the target object in terms of the reference coordinatesystem in which the calibration points are defined. This matrix is usedin the calculation of the 3-D positions of additional measured pointsdefined in the same reference frame as the calibration points. But inorder for the calibration matrix to represent a specific coordinatesystem associated with the target object, the coordinates in calibrationpoints (defined in that reference frame) need to be known. If thosepoints are not known, which is often the case, then the requiredcalibration matrix is also unknown. The process described herein seeksto solve for the difference in location (i.e., position and orientation)of a set of points, and with this process the initial calibration matrixthat is used is irrelevant—as long as it is a valid 4×4 homogeneoustransformation matrix and the reference frame is known. For this method,a default setting for the matrix (e.g., an identity matrix) is usedduring the initial measurement of the target point positions. Thisresults in the measured points being defined in terms of the LPSinstrument reference frame. Next, the points are transformed into thereference frame of the initial location of the set of points, afterwhich the difference to the next location is computed.

The process described here can be used to determine: (1) the locationoffset (hereinafter the terms “location offset” and “locationdifference” will be used interchangeably as synonyms) for moved sets ofpoints or equivalently the displacement of the LPS instrument if it hasmoved relative to the points; (2) returning to the same set of points ifeither the points or the LPS has moved (or both at the same time); and(3) measuring the location offset between multiple sets of moved points.The details of each of these variations will be discussed next.

Process for Measuring the Location Offset When a Set of Points or theLPS has Moved:

FIG. 1 shows a physical setup in which an LPS is aimed at a targetobject 10 for using a basic difference measurement method in accordancewith one embodiment. The LPS comprises a single video camera 40 and alaser range meter (not shown) on a controllable pan-tilt mechanism 42with angle measurement capability mounted on a tripod 44. The videocamera 40 may have automated (remotely controlled) zoom capabilities.The video camera 40 may additionally include an integral crosshairgenerator to facilitate precise locating of a point within an opticalimage field display of the video camera. The video camera 40 andpan-tilt mechanism 42 may be operated by a computer (not shown in FIG.1, but see LPS computer 48 in FIG. 6). The computer communicates withthe video camera 40 and the pan-tilt mechanism 42 through avideo/control cable. Alternatively, the computer may communicate withvideo camera 40 and pan-tilt mechanism 42 through a wirelesscommunication pathway. The pan and tilt angles of the pan-tilt mechanism42 and, therefore, the orientation of the video camera 40 can becontrolled using the keyboard of the computer or other input device. Theoptical image field, with crosshair overlay, as sighted by the videocamera 40, can be displayed on the monitor of the computer.

The pan-tilt mechanism 42 is controlled to positionally adjust the videocamera 40 to selected angles around a vertical, azimuth (pan) axis and ahorizontal, elevation (tilt) axis. A direction vector 12, that describesthe orientation of the camera relative to the fixed coordinate system ofthe tripod 44 (or other platform on which the pan-tilt unit isattached), is determined from the pan and tilt angles, as well as theposition of the center of crosshair marker in the optical field when thecamera is aimed at a point of interest. This direction vector 12 can bedepicted as a line extending from the lens of the camera 40 andintersecting a location on the target object 10.

A laser range meter may be incorporated inside the housing of camera 40or mounted to the outside of camera 40 in such a way that it transmits alaser beam along the direction vector 12. The laser range meter isconfigured to measure distances to the target object 10. The laser rangemeter may have a laser and a unit configured to compute distances basedon the laser light detected in response to a laser beam reflected by thetarget object 10.

The local positioning system shown in FIG. 1 further comprisesthree-dimensional localization software which is loaded into thecomputer (not shown). For example, the three-dimensional localizationsoftware may be of a type that uses multiple non-collinear calibrationpoints 14 a-14 c on the target object 10 to define the location(position and orientation) of video camera 40 relative to the targetobject 10. Typically calibration points are selected which correspond tofeatures that can be easily located on the target object 10.

The measured distances to the calibration points 14 a-14 c may be usedin coordination with the pan and tilt angles from the pan-tilt mechanism42 to solve for the camera position and orientation relative to thetarget object 10. A method for generating an instrument to targetcalibration transformation matrix (sometimes referred to as the camerapose) is disclosed in U.S. Pat. No. 7,859,655. Using the measured data,the calibration process computes the 4×4 homogeneous transformationmatrix that defines the position and orientation of the video camera 40(and laser range meter) relative to the target object 10.

Once the position and orientation of the video camera 40 with respect tothe target object 30 have been determined and a camera posetransformation matrix has been generated, camera pan data (angle ofrotation of the video camera 40 about the azimuth axis) and tilt data(angle of rotation of the video camera 40 about the elevation axis) maybe used in conjunction with the calculated position and orientation ofthe video camera 40 to determine the X, Y and Z coordinates of any pointof interest on the target object 30 in the coordinate system of theinitial location of the target object 10.

In accordance with the setup shown in FIG. 1, either the target object10 can be moved from Object Position 1 to Object Position 2 while theLPS is stationary, or the LPS can be moved from Measurement InstrumentPosition 1 to Measurement Instrument Position 2 while the target object10 is stationary. In either case, relative location data (position andorientation) can be acquired.

FIG. 2 shows steps of a method in accordance with one embodiment formeasuring the location offset or difference when either the targetobject 10 or the LPS is moved. First, the system determines the X, Y, Zvalues for the three measured points 14 a-14 c when the target object 10and the LPS are at their initial locations (step 22). Then the systemdetermines the X, Y, Z values for the three measured points 14 a-14 cafter either the target object 10 or the LPS has been moved to a newlocation (step 24). These values are input into a relative localizationprocess 20 which processes the X, Y, Z values for the initial and movedlocations and then outputs relative location data (step 26).

FIG. 3 is a flowchart showing steps of a process in accordance with oneembodiment for measuring the location difference when the target object10 is moved. (A similar process applies when the LPS instrument, not thetarget object is moved.) First, a set of three non-collinear points onthe target object 10 is specified or a set of markers are attached tothe target object 10 at a set of three non-collinear points (step 50).Then the coordinates (i.e., the X, Y, Z values) of the threenon-collinear points are measured using the LPS instrument (step 52).The measurement results (i.e., the location measurement data) are storedin memory that is accessible to the LPS computer (not shown in FIG. 1).Following this first set of measurements, the target object 10 is moved(step 54). Then the coordinates of the same points are measured againusing the LPS instrument (step 56). Again the measurement results arestored in memory. Thereafter the offset position and orientation of thetarget object 10 (this will be discussed in detail later) are computed(step 58) by the LPS computer, which retrieves and processes the storedmeasurement data. The results are displayed to the user or sent to otherapplication(s) (step 60).

Some use cases for this process include setting the position andorientation offset for a workpiece in a manufacturing workcell orinspection application. An example of the use of this process could befor object-to-robot alignment in a robotic workcell, where large partsor a robot are moved relative to each other before starting and assemblyor inspection task. In one such application the robot may be programmedto move its end effector along a specific path relative to the workpiece(target object) in the workcell. But the location of the workpiecerelative to the robot may be variable, and subsequent workpieces of thesame type may not be in the same location as the initial workpiece thatwas used during initial programming of the robot. In this situation, ifthe difference between the location of the current workpiece and thelocation of the initial workpiece were known, the offset could be sentto the robot and used as a base or origin location offset in the robotcontrol program. The process described above with reference to FIG. 3can be used to address this type of application.

The steps shown in FIG. 3 were described in terms of a moved set ofpoints, but the method also works for the case where the LPS instrumenthas moved and the location displacement of the instrument is required.Note that if both the set of points and the LPS instrument have moved atthe same time, then the reference frame displacements of the pointsrelative to the starting location of the points and the displacement ofthe LPS instrument relative to its starting location cannot bedetermined with this version of the method. Either one or the other musthave a common frame of reference with its initial location in order forthis variation of the method to work. For the case when both have moved,then the multiple moving objects process (described later) may be used.

The details of how the set of points are used in the locationdisplacement algorithm will be discussed next with reference to thevector diagram of FIG. 4.

The position and orientation offset determination process starts withspecifying or placing a set of three non-collinear points on the targetobject to be measured by LPS. In one embodiment of the reference framedefinition process, one of the points in the set of points may bedefined as the origin, another specified as one of the coordinate axes(such as the x-axis), and the third point may be used in specifying thedirection of one of the orthogonal axes (such as the z-axis) using avector cross product calculation. A third axis that is orthogonal to theother two will be determined using another vector cross product step.These steps are shown in Eqs. (1) below:

$\begin{matrix}{{{\overset{\rightharpoonup}{v}}_{1} = {{\overset{\rightharpoonup}{p}}_{1} - {\overset{\rightharpoonup}{p}}_{0}}}{{\overset{\rightharpoonup}{v}}_{2} = {{\overset{\rightharpoonup}{p}}_{2} - {\overset{\rightharpoonup}{p}}_{0}}}{{\hat{v}}_{x} = \frac{{\overset{\rightharpoonup}{v}}_{1}}{v_{1}}}{{\overset{\rightharpoonup}{v}}_{y} = {{\overset{\rightharpoonup}{v}}_{2} \times {\overset{\rightharpoonup}{v}}_{1}}}{{\hat{v}}_{y} = \frac{{\overset{\rightharpoonup}{v}}_{y}}{{\overset{\rightharpoonup}{v}}_{y}}}{{\hat{v}}_{z} = {{\hat{v}}_{x} \times {\hat{v}}_{y}}}} & (1)\end{matrix}$

The process begins by defining vectors {right arrow over (v)}₁ and{right arrow over (v)}₂ using the three measured points {right arrowover (p)}₀, {right arrow over (p)}₁ and {right arrow over (p)}₂ from theinitial measured location, then computing the orthogonal unit vectors{circumflex over (v)}_(x), {circumflex over (v)}_(y) and {circumflexover (v)}_(z) (see FIG. 4). These three orthogonal unit vectors will beused to create columns of a 3×3 rotational matrix (also known as adirection cosine matrix) as shown below:

$\begin{matrix}{{Rot} = \begin{bmatrix}{\hat{v}}_{x\; 1} & {\hat{v}}_{y\; 1} & {\hat{v}}_{z\; 1} \\{\hat{v}}_{x\; 1} & {\hat{v}}_{y\; 2} & {\hat{v}}_{z\; 2} \\{\hat{v}}_{x\; 3} & {\hat{v}}_{y\; 3} & {\hat{v}}_{z\; 3}\end{bmatrix}} & (2)\end{matrix}$

The changes in position (ΔX, ΔY and ΔZ) for the origin point areincluded as the last column, with 0,0,0,1 as the last row, resulting ina 4×4 homogeneous transformation matrix, shown below:

$\begin{matrix}{{\,_{1}^{0}T} = \begin{bmatrix}r_{11} & r_{12} & r_{13} & {\Delta \; X} \\r_{21} & r_{22} & r_{23} & {\Delta \; Y} \\r_{31} & r_{32} & r_{33} & {\Delta \; Z} \\0 & 0 & 0 & 1\end{bmatrix}} & (3)\end{matrix}$

where r₁₁ through r₃₃ are the elements of the 3×3 rotation matrix shownin Eq. (2). The 4×4 matrix of Eq. (3) defines the initial state of theset of points (reference frame {1}) relative to the internal coordinatesystem of the LPS instrument (reference frame {0}).

Initially both sets of measured points are defined relative to thearbitrary reference frame {0}, which was set as the origin of the LPSinstrument, but in order to compute the position and orientation offsetsrelative to the first set of points (i.e., reference frame {1}), themeasured points will be pre-multiplied by the 4×4 matrix described inEq. (3), as shown below:

¹ P _(i,j)=₀ ¹ T ⁰ P _(i,j)  (4)

where the subscripts i, j represent the individual points in each set ofpoints.

With the two sets of vectors defined in terms of the coordinate systemof the first set of points, the differences in position and orientationbetween the two sets of points (one set having a local coordinate systemA and the other set having a local coordinate system B) can be computed.This difference calculation is performed with a simpleelement-by-element subtraction for the initial location (a) andsubsequent locations (b, c, etc.), for example:ΔP_(i,j)=^(b)P_(i,j)−^(a)P_(i,j).

For situations where the reference points are not aligned along specificaxes, the process for aligning vectors described in U.S. Pat. No.7,859,655 may be used. In this situation, since there is no pre-definedreference coordinate system for the object, the method uses theinstrument coordinate system as the frame of reference.

Start defining two vectors for each set of points (vector indicationsremoved for clarity):

V _(A12) =P _(A2) −P _(A1)

V _(A13) =P _(A3) −P _(A1)

V _(B12) =P _(B2) −P _(B1)

V _(B13) =P _(B3) −P _(B1)  (5)

Then compute the transformation matrix describing the rotation from oneset of vectors to the other:

n _(p) =V _(A12) ×V _(A13)

n _(B) =V _(B12) ×V _(B13)

axis ₁ =n _(A) ×n _(B)

ang ₁=arccos(|n _(A) |·|n _(B)|)

Rot ₁ =f ₁(ang ₁ ,axis ₁)

axis ₂ =V _(A12) ×V _(B12)

ang ₂=arccos(|V _(A12) |·|V _(B12)|)

Rot ₂ =f ₁(ang ₂ ,axis ₂)

Rot ₁₂ =Rot ₁ *Rot ₂

_(B) ^(A) T=[Rot ₁₂ ,Rot ₁ *V _(B12) −V _(A12)]

_(B) ^(A) T=(_(A) ^(B) T)⁻¹  (6)

where f₁( ) is the function which generates a 3×3 rotation matrix fromthe angle-axis definition (described in detail by Craig, J. J., in“Introduction to Robotics: Mechanics and Control”, Addison-Wesley,1986). Note that _(A) ^(B)T only needs to be computed once for anyposition of the measurement device relative to the target object, andcan then be used to convert any number of vectors from coordinate systemA into coordinate system B.

The result of the foregoing calculations is an angle-axis representationthat is converted into a 4×4 homogeneous transformation matrix thatdescribes the position and orientation offsets of the set of points atthe second location relative to the set of points at the first location,and defined in the coordinate system of the first location of the set ofpoints.

To finish the process, the origin offset values (ΔX_(AB), ΔY_(AB) andΔZ_(AB)) are included as the last column, in the same way as shown inEq. (3). The resulting 4×4 homogeneous transformation matrix describesthe offset of the second location relative to the first location interms of the coordinate system of the first location.

Multiple locations of the object relative to its initial position can behandled with repeated usage of the same process outlined above. And thesame type of solution is also applicable to the situation were the LPSinstrument is moved. Moving a set of points from one location to anotheror moving the measurement instrument is equivalent from thecomputational aspect of the process, but the use case andimplementations may be different. The details of a variation of thisprocess for re-targeting a sequence of points of interest will bediscussed next.

Recalibration of LPS to Re-Target a Set of Points when the LPSInstrument and/or the Set of Points have Moved:

The relative displacement measurement process described above wasexplained in terms of a moving set of points from one location toanother or equivalently, moving the LPS instrument. An extension of thisprocess for visual indication of multiple points on a target object isto instruct the LPS instrument to aim (i.e., point its laser and camera)at the same set of points that were recorded in a prior session afterthe set of points, the LPS instrument, or both have been moved. This isuseful in cases when a user records 3-D measurements of a set of pointson a target object—which would include the three calibration points, aswell and any other points of interest—and then wishes to return to them(i.e., aim the LPS laser at the points) at a future time when theplacement of the LPS instrument relative to the target object may havechanged. For this type of re-targeting use case, the displacement matrixis computed and will be used to pre-multiply the existing LPScalibration matrix, as shown in Eq. (7):

M _(new) _(—) _(cal) =M _(diff) M _(old) _(—) _(cal)  (7)

In Eq. (7), M_(old) _(—) _(cal) may be a 4×4 homogeneous transformationmatrix (computed using the standard three-point LPS calibration processdisclosed in U.S. Pat. No. 7,859,655) that describes the position andorientation of the coordinate system of a target object relative to theLPS instrument. In other situations, M_(old) _(—) _(cal) may be anarbitrary 4×4 homogeneous transformation matrix, such as the identitymatrix associated with the relative location method described earlier.When the user moves the LPS, or equivalently when the target objectmoves, or if both LPS and the target have moved, the goal is to computea new calibration matrix M_(new) _(—) _(cal) based on the relativeposition and orientation of the LPS and the target object. Thedisplacement matrix M_(diff) in Eq. (7) describes this relative positionand orientation difference and is computed using the process describedin Eqs. (5) and (6). M_(diff) is used to modify the original LPScalibration matrix M_(old) _(—) _(cal) in order to create a newcalibration matrix M_(new) _(—) _(cal). The resulting matrix can then beused as the new LPS calibration matrix. After this recalibration step,the user will be able to instruct LPS to aim at the list of pointsregardless of where the LPS instrument has moved to (as long as the aimpath is not occluded).

In this process the operator will select three visible features or placethree markers on the target object as calibration points (which shouldbe non-collinear and spaced as far apart as practical), and then measureother points of interest on the target object in its first position. Thegoal will be to return to all of the same points after the LPSinstrument has been moved to a different location. In this usagescenario, the three calibration points should be easy to locatevisually, but the rest of the points of interest do not have to be. Forexample, the three calibration points may be corners of an airplanewindow, and the other points of interest may be points, such as rivetlocations, that may be painted over and not visible at a later time.

The individual steps for the points of interest re-targeting process areshown in FIG. 5. First, the operator specifies or places three visible,non-collinear points on the target object to be used as calibrationpoints (step 62). The operator may specify one or more additional pointsof interest on the target object. The coordinates of those calibrationpoints and any points of interest are then measured using the LPSinstrument (step 64). The measurement results are stored in memory.Thereafter the LPS instrument is moved to a different location relativeto the target object (step 66). Then the coordinates of the samecalibration points on the target object are measured again using the LPSinstrument (step 68). The measurement results are again stored in memoryThe LPS computer then computes the offset position and orientation ofthe LPS device, and applies the resulting transformation matrix (i.e.,M_(diff) in Eq. (7)) to the existing calibration matrix (i.e., M_(old)_(—) _(calc) in Eq. (7)) (step 70 in FIG. 5). The LPS is then instructedto play through the series of points of interest (which involves the LPSautomatically aiming at each of the points of interest defined in step62).

Note that the “existing calibration matrix” may be the identity matrix,but in some cases it will not be. For example, the original calibrationmatrix may have been created using some other method (like the originalLPS method disclosed in U.S. Pat. No. 7,859,655) or for the relativemotion usage case, the current location of the object may not be thesecond location, but rather the third or fourth, etc., in which case theexisting calibration matrix may have been the result of multiplyingprior differences matrices. So while the calibration matrix may havestarted as an identity matrix, it may have been modified prior to thelatest location change, in which case the “existing calibration matrix”may currently be something other than an identity matrix.

The foregoing process may also be used in situations where two similartarget objects are at different sites A and B. An operator at site Atargets three visible calibration points and any number of other pointsof interest on the target object at site A, and then saves all of thepoints in a file. The operator at site A then sends the point file to anoperator at site B and instructs the operator at site B to measureinstances of the same three visible features on the target object atsite B. The operator at site B instructs the LPS instrument at site B torecalibrate using this data (i.e., the points data from site A and siteB).

When the LPS re-calibration process is used by the operator at site B,the data at site B will be produced by that site's LPS instrument in thecoordinate system used by the LPS measurements made at site A. Forexample, if the measurements at site A were in target objectcoordinates, then the site B results will be in target objectcoordinates. Alternatively, if the operator at site A used the internalreference coordinate system of the LPS instrument, then the LPSinstrument at site B will be re-calibrated to the frame of reference ofthe LPS instrument at site A. The LPS re-calibration process at site Buses the LPS calibration matrix from site A and produces a differencematrix describing the location of the LPS instrument at site B relativeto the target object-to-LPS location at site A.

The LPS calibration matrix is derived from a set of Cartesian andspherical coordinate points, so optionally, if the operator at site Asent both types of point files to site B, then the LPS software at siteB can re-compute the original calibration matrix, but it is alsopossible to send the original calibration matrix directly, along withthe Cartesian point file.

Upon completion of the LPS re-calibration process at site B, theoperator at site B may then instruct the LPS instrument at site B toplay through the points of interest sent by the operator at site A. TheLPS instrument at site B will then aim its laser at the same pointsmeasured by the operator at site A, even though the LPS instrument atsite B is in a different location relative to the target object at siteB. This data sharing and calibration process effectively synchronizesthe respective LPS instruments at sites A and B.

Optionally, the operator at site B may want to send additional pointsback to the operator at site A, which by following the same process,would synchronize the LPS instrument at site A with the LPS instrumentat site B. The transfer of the point data files between the two sitescould happen in real-time (such as with a socket interface over anetwork connection), or delayed in time, such as would happen withe-mail or sending a copy of the data, which could be on physical media(like a compact disk).

This process enables the transfer of calibration from one LPS instrumentto another. It could be useful in communicating the locations of pointsof interest between two or more operators working on similar targetobjects. In accordance with this remote usage concept, two (or more)separate LPS instruments will be sharing a set of data points, eventhough the LPS instruments will be in different locations with respectto their respective target objects.

There are multiple ways that this concept can be implemented, includinghaving the calibration points targeted in a separate step or making thecalibration points part of the same dataset that contains all of thepoints of interest (such as using the first three points or the lastthree points in the sequence). In one implementation of this concept,all of the points are stored in the same file.

The synchronization process described above has some similarities withthe remote operation of an LPS that is described in U.S. Pat. No.8,447,805 and U.S. Patent Application Pub. No. 2012/0327187, but theprocess described here is much simpler to implement and use, since itdoes not require either known 3-D data points or a real-time dataconnection, and it provides an easy-to-use process that addressesdistance separation as well as tasks that are separated in time (byseconds, days, or even years).

Process for Measuring Location Offsets for Multiple Moving Objects:

The method for determining location displacement disclosed above alsoenables the determination of the position and orientation of one targetobject relative to another using only a single, portable measurementdevice and visible reference features on the target objects.

Up to this point, the discussion of the method for determining locationdisplacement has involved one object (with a set of three visible,non-collinear features) and an LPS instrument, but the range of usagescenarios can be extended to address multiple moved objects through theuse of multiple applications of the method. This approach will enableadditional types of relative displacement use cases in situations withtwo or more moved objects (each with its own set of visible referencepoints arranged in the same configuration).

FIG. 6 shows steps of a method in accordance with one embodiment formeasuring the location offset between two workpieces (e.g., Part 1 andPart 2) when either or both parts have moved relative to an LPSinstrument. First, the system determines the X, Y, Z values for threemeasured points on Part 1 and the X, Y, Z values for three measuredpoints on Part 2 when these parts are at their respective initiallocations (steps 22 a and 22 b). The three measured points on Parts 1and 2 may be arranged in the same or different configurations, so longas the three reference points in each set are not collinear. After Parts1 and 2 are moved to new locations, again the system determines the X,Y, Z values for the same measured points on Parts 1 and 2 (steps 22 aand 22 b). All of these values are input into a relative localizationprocess 20 a which processes the X, Y, Z values for the respectiveinitial and moved locations of Parts 1 and 2, and then outputs relativelocation data (step 26 a).

The foregoing variation of the method for determining locationdisplacement can be used to compute the location change of one or moreobjects from a reference object, even if the location of the LPSinstrument has changed. This capability can be used to addresssituations where two or more independent objects may move relative toeach other, and where one or more of them may have moved relative to thelocation of a respective LPS instrument. Since this form of the methodis addressing relative displacement between the two (or more) objects,the process is independent of LPS instrument location change.

And if it is known that the location of the LPS instrument has notchanged, or if the location offset of the LPS instrument from itsinitial location is known, then the location of all of the moved objectsrelative to the reference object in its initial location can bedetermined.

It has already been discussed that the location of the LPS instrumentrelative to a stationary object can be determined; and in the scenariowherein two objects have moved, the LPS instrument has moved, and onestationary object is available, the relative displacement of the movedobjects can be determined with respect to the location of one of theobjects in its initial position.

An example of this type of use case is a robotic workcell where thedisplacement of the robot relative to a workpiece is required, but theworkpiece, the robot, and the LPS instrument may have all been movedfrom prior locations when the robot was initially programmed. Forexample, the techniques disclosed above can be used to determine theposition and orientation of a robotic arm relative to a workpiece(hereinafter “part”) in such a situation.

As shown in FIG. 7, the LPS in accordance with one embodiment comprisesa video camera 40 and a laser range meter (not shown) on a controllablepan-tilt mechanism 42 mounted on a tripod 44. The video camera 40 andpan-tilt mechanism 42 are operated by an LPS computer 48. The LPScomputer 48 communicates with the video camera 40, laser range meter,and the pan-tilt mechanism 42 through a video/control cable 46. The panand tilt angles of the pan-tilt mechanism 42 and, therefore, theorientation of the video camera 40 can be controlled using the keyboardof the computer or some other input device, such as the gamepadinterface 36 shown in FIG. 7. The optical image field, with crosshairoverlay, as sighted by the video camera 40, can be displayed on themonitor 34 of the computer 48.

The LPS seen in FIG. 7 can be used to determine the relative offsetbetween a part 90 and the base 84 of a robotic arm 86 that may carry anend effector 88 on a distal end thereof. The robot controller 80controls the robotic arm 86 and operates the end effector 88 forperforming machining or other operations on the part 90. The LPScomputer 48 communicates with the robot controller 80 through a cable78. The robot controller 80 is preferably a computer programmed withmotion control software whereby the location of end effector 88 can becontrolled as a function of object location data output by the LPScomputer 48.

The location offset between base 84 and part 90 can be determined in themanner previously described with reference to FIG. 6. First, the LPScomputer 48 determines the X, Y, Z values for measured points 92 a-92 con part 90 and the X, Y, Z values for measured points 94 a-94 c on base84 when base 84 and part 90 are at their respective initial locations.After base 84 and part 90 have moved to new locations, again LPS is usedto determine the X, Y, Z values for measured points 92 a-92 c and 94a-94 c. The LPS system 48 the uses a relative localization process toproduce data representing the location of the part 90 relative to thebase 84 at their new locations. This data is output to the robotcontroller 80 via cable 78.

The foregoing methodology can be used at the start of each work sequenceto establish the relative positions of the base 84 of the robotic arm 86and the part 90. The robot controller 80 will be able to compute theposition and orientation of the end effector 88 relative to the robotbase 84 (using other sensors and kinematics data).

Commercial robotics applications used for production tasks have aprocess to define the location of the robot and other parts relative tothe origin of the workcell. This will include both position andorientation offset definitions. There are many equivalent ways to definethis offset information, such as: 4×4 transformation matrices,quaternions and translation, angle-axis and translation, or Euler anglesand translation. The localization process described herein can bemodified to output in whatever format is acceptable to the robotcontroller 80.

There are several options that may be used to transfer the data from thecomputer 48 to the robot controller 80; some controllers may have anapplication programming interface (API) that accepts incoming data overa network socket or through a serial interface; other controllers mayonly allow offset data to be read from a file. Accordingly, inaccordance with some embodiments, a file sharing approach can be used.

The steps of a method of measuring the location offset or differencebetween two moving objects (such as the base 84 and the part 90 depictedin FIG. 7) are outlined in FIG. 8. First, a set of three non-collinearpoints on a first target object (Object 1 in FIG. 8) is specified or aset of markers are attached to the first target object at a set of threenon-collinear points (step 100); and then a set of three non-collinearpoints on a second target object (Object 2 in FIG. 8) is specified or aset of markers are attached to the second target object at a set ofthree non-collinear points (step 102). Then the coordinates of the threenon-collinear points on both objects are measured using the LPSinstrument (step 104). (The respective frames of reference of the LPSinstrument and the first and second target objects are indicated by {0},{1}, and {2} in FIG. 9.) The measurement results are stored in memory.The LPS computer then computes the location difference between the twosets of points (step 106) based on the measurement results in step 104,defined in the reference frame of one of the objects (as describedabove), and stores this location difference in memory (e.g., as a 4×4transformation matrix). (As used herein, the phrases “locationdifference” and “offset position and orientation” are synonymous.)

Following this first set of measurements, one or both of the objectsand/or the LPS instrument can be moved (step 108). FIG. 9 depicts asituation wherein all three have been moved, the LPS instrument movingfrom reference frame {0} to reference frame {0}′, Object 1 moving fromreference frame {1} to reference frame {1}′, and Object 2 moving fromreference frame {2} to reference frame {2}′.

After the objects and LPS are moved, the coordinates of the same pointson Objects 1 and 2 are measured again with respect to frames ofreference {1}′ and {2}′ using the LPS instrument (see step 110 in FIG.8). Again the measurement results are stored in memory. The LPS computerthen computes the location difference between the two new sets of points(step 112) based on the measurement results in step 110 (defined in thereference frame of the same object that was selected in step 106), andstores this location difference in memory (e.g., as another 4×4transformation matrix). Then the LPS computer computes the differencebetween the stored location differences found in steps 106 and 112.

Additional objects may also be included in the foregoing process, ifnecessary.

In the robotic workcell example described above with reference to FIG.7, the location differences found in step 114 above would be used by therobot controller to determine its new base offset value of the robotrelative to the workpiece. In this situation, the LPS instrument wouldbe represented by reference frame {1} and {1}′, the robot by referenceframe {2} and {2}′, and the workpiece by reference frame {3} and {3}′(as shown in FIG. 9). To determine the required change for the robotbase offset value, it is important to note reference frames {2} and {2}′can be considered to be coincident. This allows the calculateddifference between workpiece locations {3} and {3}′ to be applied to therobot base offset in the current location of the robot {2}′.

In another embodiment of this variation of a process with multipleapplications of the difference method, if the absolute offset isrequired for a moved object when the LPS instrument has also been moved,an additional set of reference points can be attached to a stationaryobject. This stationary object would take the place of the frame ofreference of the object selected in step 106.

The position and orientation differences between multiple separateobjects can also be determined if those objects have a visible featurethat can serve as a direction reference.

Modifying Existing LPS Applications to Use the Capability DisclosedHerein:

The LPS use case described in U.S. Pat. No. 7,859,655 requirescalibration with respect to a specific coordinate system associated withthe target object, but not all applications need to have measurements inabsolute coordinates. Some types of use cases developed for the LPS thatare currently based on knowing local calibration coordinates on thetarget object can be modified for use with the method disclosed hereinif the application can be based on displacement relative to a startingpoint. For example, in the application to track the position andorientation of a crawler vehicle described in U.S. patent applicationSer. No. 13/921,246, the LPS was calibrated to the coordinate system ofthe target object and instructed to measure the position and orientationof the robotic crawler as it moved to different inspection locations onthe target object. That process works well if calibration coordinatesare known, but in some cases 3-D point data is not available, such asfor older airplanes designed without the use of CAD models. For thesecases, operators would still like to be able to use the LPS formeasurement tasks.

The relative measurement method disclosed herein cannot be used toindicate a location on the target object defined in the coordinatesystem of the target object, as would be required to direct a crawlervehicle to a specific starting point. But if the crawler vehicle couldbe moved to a desired starting location separately, the relativelocalization method described here can be used to track the crawlervehicle relative to its starting location. This modified localizationmethod cannot completely replace the original LPS usage, but in somecases the problem can be reformulated to allow it to be solved as arelative displacement problem.

Point-to-Point Measurement:

Some simple measurement tools, like tape measures or measurement wheels,require an unobstructed path between measurement points. These types ofdevices also require contact with the surface of the target object.Other measurement devices such as surveying equipment hand-held laserrange meters may have software to compute distances, but they do nothave object orientation measurement capabilities.

The methodology disclosed herein measures object locations in terms ofposition and orientation, but can also handle simple position-onlymeasurements. It can be used to compute translation and orientationdisplacement, can handle situations with obstructions between themeasurement points, and does not require contact with the target object.These types of use cases are problematic for measurements with tapemeasures or measuring wheels.

This simple point-to-point measurement mode addresses distance betweenpoints, as well as vector-based measurement. For example, a user mayhave a requirement to “start here and mark a spot 200 inches in thatdirection, turn 90 degrees and mark another spot 100 inches from there,etc.” The point-to-point process can also be used to measure perimetersor indicate positions on the surface of a target object using the LPSlaser without contacting the surface.

Other Uses:

Post-Measurement Alignment:

Having measurements defined in the coordinate system of the targetobject is still going to be important for some applications, but in somesituations it may not be necessary to know what the target coordinatesare for the measured points while the points are being measured. Forthese situations the data points acquired with LPS in the relativemeasurement mode can be aligned with known 3-D data points (such as CADmodel data) at a later time if that data becomes available. This allowsthe LPS operator to use LPS in the simpler relative position acquisitionmode, with the operator taking pictures of the feature points (orindicating them in another way) to use in the future for 3-D modelalignment. Then at a later time an analyst can align the feature pointswith 3-D model data of the target object and then convert all of theacquired data points into the coordinates of the target object.

Automation:

In the manual operation mode the user directs the LPS instrument to aimat the visible calibration features on the target object, but if activetarget markers, such as LEDs, are placed on the target object (asdisclosed in U.S. patent application Ser. No. 13/921,246), then themeasurement procedure can be automated. This works by using images fromthe LPS camera and an image processing differencing method to detect theactive markers (LEDs) on the target. These marker locations will then beused to direct the LPS instrument to aim at the targets to acquiredistance information for the required number of points (three) for usewith the location difference method disclosed herein. With the use ofactive markers, the location difference method can be performed by afully automated system.

Data Transfer:

The measurement results can be computed and sent to other applications.A measurement system of the type described above can be connected toother applications through a serial or network socket connection. Thisallows communication between the applications to send the results of themeasurements, or other process events, such as instructing an LPS whento initiate the process. For example, this process can provide baselocation information to a robotic arm used in a manufacturingapplication.

Capturing Trends:

Acquiring position data for a large set of visible features on differentinstances of the same model of a target object, such as an airplane,would provide the raw data needed for statistical analysis. For example,this data could be used to determine trends for manufacturing qualitycontrol, or in-use check-ups (such as for fatigue or deformationanalysis for failure prediction). The data can be aligned to a commonreference frame using the post-measurement 3-D model alignment processdisclosed above or using the basic relative differencing methoddisclosed earlier.

Use of the relative object localization process disclosed herein isespecially important when 3-D data is not available, too hard to access,or difficult to work with (i.e., manipulating files, and not makingmistakes). In some cases, where 3-D data points were required to use theoriginal LPS process, this relative measurement mode could be usedinstead. This can reduce or eliminate the preparation time needed forthose cases. For some LPS applications a set of known 3-D points willalways be needed in order to give results in the proper coordinatesystem of the target object, but this new relative measurement modeopens up a new class of applications that were previously out of scopefor LPS due to the requirement for known data points.

The above-described relative object localization process would bevaluable to persons who perform measurements on objects without accessto known 3-D reference point data. This includes industrial applicationslike manufacturing and inspection, where 3-D data may not be availableor is difficult to acquire. These types of applications could be inareas such as: aerospace, architecture, construction, shipbuilding, andvarious types of forensics.

The relative object localization process also applies to consumer-levelapplications, where 3-D data is almost never available. For the averageconsumer the most common measurement instrument is a simple tapemeasure, which is difficult to use for moderate to complex measurementactivities. The consumer-level applications could include indoor oroutdoor uses, such as: measuring a room or the dimensions of a driveway,hanging a set of pictures on a wall in a specific configuration,indicating sewing patterns on pieces of cloth, laying out a baseballdiamond, transferring a small-scale design or model to full-scale (orvice versa), etc.

While relative object localization processes have been described withreference to various embodiments, it will be understood by those skilledin the art that various changes may be made and equivalents may besubstituted for elements thereof without departing from the scope of theteachings herein. In addition, many modifications may be made to adaptthe concepts and reductions to practice disclosed herein to a particularsituation. Accordingly, it is intended that the subject matter coveredby the claims not be limited to the disclosed embodiments.

As used in the claims, the term “computer system” should be construedbroadly to encompass a system having at least one computer or processor,and which may have multiple computers or processors that communicatethrough a network or bus. As used in the preceding sentence, the terms“computer” and “processor” both refer to devices comprising a processingunit (e.g., a central processing unit) and some form of memory (i.e.,computer-readable medium) for storing a program which is readable by theprocessing unit.

As used in the claims, the term “location” comprises position in a fixedthree-dimensional coordinate system and orientation relative to thatcoordinate system.

The method claims set forth hereinafter should not be construed torequire that the steps recited therein be performed in alphabeticalorder (alphabetical ordering in the claims is used solely for thepurpose of referencing previously recited steps) or in the order inwhich they are recited. Nor should they be construed to exclude anyportions of two or more steps being performed concurrently oralternatingly.

1. A method for determining a current position of a target objectrelative to an initial location of the target object, said methodcomprising: (a) selecting a set of at least three points on a targetobject; (b) placing the target object at an initial location withinmeasurement range of a positioning system having a non-occluded view ofthe target points; (c) measuring respective coordinates of three pointsof said set of points associated with the target object in a frame ofreference of the positioning system while the target object is at theinitial location; (d) moving the target object from the initial locationto a current location; (e) measuring respective coordinates of saidthree points associated with the target object in the frame of referenceof the positioning system while the target object is at the currentlocation; and (f) computing a position difference in a frame ofreference of the initial location of the target object based on resultsof steps (c) and (e), said position difference representing a differencebetween the initial and current positions of the target object in theframe of reference of the initial location of the target object.
 2. Themethod as recited in claim 1, wherein step (f) further comprisescomputing an orientation difference in the frame of reference of theinitial location of the target object based on the results of steps (c)and (e), said orientation difference representing a difference betweenthe initial and current orientations of the target object in the frameof reference of the initial location of the target object.
 3. The methodas recited in claim 2, further comprising displaying results of step (f)to a user.
 4. The method as recited in claim 2, further comprisingsending results of step (f) to an application.
 5. The method as recitedin claim 2, wherein the number of points selected in step (a) is greaterthan three, step (c) further comprises measuring coordinates of a fourthpoint, and said method further comprises: computing a transformationmatrix that defines the offset of the current location of the targetobject relative to the initial location of the target object; andmultiplying the coordinates of said fourth point by said transformationmatrix.
 6. A method for determining a position of one target objectrelative to another target object, said method comprising: (a) selectinga set of at least three points on a first target object; (b) placing thefirst target object at a first location within measurement range of apositioning system having a non-occluded view of the target points onthe first target object; (c) measuring respective coordinates of threepoints of said set of points on the first target object in a frame ofreference of the positioning system while the first target object is atthe first location; (d) selecting a set of at least three points on asecond target object; (e) placing the second target object at a secondlocation within measurement range of a positioning system having anon-occluded view of the target points on the second target object; (f)measuring respective coordinates of said three points on the secondtarget object in the frame of reference of the positioning system whilethe second target object is at the second location; and (g) computing afirst location difference in a frame of reference of the first locationof the first target object based on results of steps (c) and (f), saidfirst location difference representing a difference between therespective locations of the first and second target objects in the frameof reference of the first location of the first target object.
 7. Themethod as recited in claim 6, further comprising: (h) moving one or bothof the first and second target objects and/or the positioning systemfrom the initial location to a current location, said current locationcomprising a current position and a current orientation; (i) after step(h), measuring respective coordinates of said three points on the firstand second target objects in the frame of reference of the positioningsystem; (j) computing a second location difference in a frame ofreference of the first location of the first target object based onresults of step (i), said second location difference representing adifference between the respective locations of the first and secondtarget objects in the frame of reference of the first location of thefirst target object; and (k) computing a third location difference in aframe of reference of the first location of the first target object,said third location difference being based on a difference between saidfirst and second location differences.
 8. The method as recited in claim6, further comprising sending the results of step (k) to a controllerthat controls the movement of one of the first and second targetobjects.
 9. A method for locating a point on a target object, saidmethod comprising: (a) placing first instances of a positioning systemand a target object at respective locations such that the first instanceof a target object is within measurement range of the first instance ofa positioning system; (b) selecting a set of at least three points onthe first instance of a target object; (c) measuring respectivecoordinates of said three points of said set of points on the firstinstance of a target object in a frame of reference of the firstinstance of a positioning system while the first instances of apositioning system and a target object are at their respectivelocations; (d) placing second instances of a positioning system and atarget object at respective locations such that the second instance of atarget object is within measurement range of the second instance of apositioning system; (e) measuring respective coordinates of three pointsof said set of points on the second instance of a target object in aframe of reference of the second instance of a positioning system whilethe second instances of a positioning system and a target object are attheir respective locations; (f) computing a displacement matrix thatrepresents the difference between the frame of reference of the secondinstance of a positioning system to the frame of reference of the firstinstance of a positioning system based on differences between themeasurement results of steps (c) and (e); and (g) computing an updatedcalibration matrix representing a transformation from the frame ofreference of the second instance of the positioning system to a frame ofreference of the second instance of the target object by multiplying acurrent calibration matrix by said displacement matrix to create theupdated calibration matrix.
 10. The method as recited in claim 9,wherein the number of points selected in step (a) is greater than three,step (c) further comprises measuring coordinates of a fourth point, andsaid method further comprises multiplying the coordinates of said fourthpoint by said displacement matrix.
 11. The method as recited in claim 9,wherein the first and second instances of the positioning systemcomprise the same positioning system at different locations.
 12. Themethod as recited in claim 9, wherein the first and second instances ofthe positioning system comprise different positioning systems atdifferent locations.
 13. The method as recited in claim 9, wherein thefirst and second instances of the target object comprise the same targetobject.
 14. The method as recited in claim 9, wherein the first andsecond instances of the target object comprise different target objectsat different locations.
 15. A method for re-calibrating a positioningsystem with respect to a target object, said method comprising: (a)selecting a set of at least three points on a target object; (b)obtaining measurement results comprising respective coordinates of saidset of points measured in the frame of reference of a positioning systemwhile the positioning system is at a first location; (c) setting up thepositioning system at a second location different than the firstlocation; (d) measuring respective coordinates of said three points ofsaid set of points on the target object in the frame of reference of thepositioning system while the positioning system is at the secondlocation; (e) computing a displacement matrix based on differencesbetween the obtained measurement results and the measurement results ofstep (d); and (f) computing an updated calibration matrix representing atransformation from the frame of reference of the positioning system atthe second location to a frame of reference of the target object bymultiplying a calibration matrix corresponding to said obtainedmeasurement results by said displacement matrix to create the updatedcalibration matrix.
 16. The method as recited in claim 15, wherein thenumber of points selected in step (a) is greater than three and saidobtained measurement results further comprise coordinates of a fourthpoint, said method further comprising multiplying the coordinates ofsaid fourth point by said updated calibration matrix.